Numerical simulation method of high cycle fatigue of circular steel tube intersection based on extended finite element

Abstract

The present invention belongs to the field of structural engineering, and specifically relates to a method for numerically simulating high-cycle fatigue of a circular steel tube intersecting node based on extended finite elements, comprising the following steps: establishing a numerical model of a circular steel tube intersecting node containing an initial crack in a software platform according to the mechanical properties and specifications of the materials used for the intersecting node specimen; defining the crack region by using the extended finite element method and the level set function to obtain the stress intensity factor at the crack front; applying loads and boundary conditions; establishing a high-cycle fatigue crack extension program for the intersecting node; implanting the high-cycle fatigue crack extension program into the software platform for calculation; processing the simulation data to obtain the extension rate curve of the fatigue crack of the intersecting node, and comparing the result with the test to verify the validity of the simulation result. The present application avoids the need for mesh reconstruction for each incremental step when the finite element method is extended to simulate this problem.

Description

Technical Field

[0001] The invention belongs to the field of structural engineering, and in particular relates to a high-cycle fatigue numerical simulation method of circular steel pipe intersecting nodes based on extended finite elements. Background Art

[0002] Intersection nodes are widely used in large-span public buildings such as large stadiums and airport terminals because they are easy to process and construct. Therefore, many scholars have studied the mechanical properties of intersection nodes to ensure their reliability during service.

[0003] Compared with low-cycle fatigue damage caused by earthquakes, high-cycle fatigue damage takes longer and has no obvious signs when it occurs, which can easily cause serious economic and property accidents. For example, the collapse of the 2E terminal at Charles de Gaulle Airport in France in 2004 was caused by the continuous expansion of cracks at the connection between the ceiling and the pillars of the terminal under the action of long-term wind loads, resulting in sudden fractures. The accident at the Alexander L.Kielland offshore platform in Norway in 1980 directly caused 123 casualties. After investigation, the cause of the accident was fatigue damage to a support rod of the offshore platform, which caused the destruction of the main load-bearing components. Therefore, it is necessary to study the expansion of high-cycle fatigue cracks at intersecting nodes.

[0004] Intersection nodes include various forms such as round steel tube intersection nodes and square steel tube intersection nodes. Currently, the commonly used numerical simulation methods for high-cycle fatigue crack growth of round steel tube intersection nodes include finite element method and boundary element method. Among them, finite element method is the most widely used and the most mature technology. The operation process of this method is as follows Figure 1 In this process, the mesh of the whole model needs to be reconstructed every time the crack expands, which greatly increases the calculation time. At the same time, the mesh reconstruction is difficult and not easy to operate.

[0005] The extended finite element method is developed on the basis of the unit decomposition method. This method does not require re-meshing when simulating fatigue crack growth, which solves the disadvantages of the finite element method in dealing with such problems. However, the existing software cannot use the extended finite element method to simulate high-cycle fatigue crack growth. Therefore, a method is needed to solve the disadvantages of the finite element method's mesh re-division, and at the same time, use the existing software as a platform to realize the application of the extended finite element method in the high-cycle fatigue crack growth of the intersecting node of the circular steel tube. Summary of the invention

[0006] The purpose of the present invention is to propose a numerical simulation method for high-cycle fatigue of circular steel tube intersecting nodes based on extended finite elements, so as to avoid the disadvantage that the finite element method requires mesh reconstruction for each incremental step when simulating this problem, resulting in low computational efficiency, and at the same time solve the problem that the existing software does not have the basic function of simulating high-cycle fatigue crack propagation of circular steel tube intersecting nodes.

[0007] The present invention is implemented by the following technical solution: a numerical simulation method for high cycle fatigue of circular steel pipe intersection nodes based on extended finite element, comprising the following steps:

[0008] Step 1: According to the mechanical properties and specifications of the materials used for the intersection node specimens, a numerical model of the intersection node of a circular steel pipe with an initial crack is established in the software platform;

[0009] Step 2: Use the extended finite element method and level set function to define the crack region to obtain the stress intensity factor at the crack front. The calculation method of the stress intensity factor is:

[0010]

[0011] In the formula, K I , K II , K III are the stress intensity factors corresponding to mode I crack, mode II crack and mode III crack respectively; J I int , J II int , J III int are the interaction J-integrals corresponding to mode I crack, mode II crack and mode III crack respectively; B is the logarithmic energy system matrix;

[0012] Step 3: Apply loads and boundary conditions;

[0013] Step 4, establishing a high-cycle fatigue crack growth program for intersecting nodes, specifically including: establishing fatigue crack growth criteria, determining fatigue crack growth direction, extracting stress intensity factor and crack front coordinates, calculating crack growth increment for the next incremental step, calculating crack front coordinates for the next incremental step, and updating crack model for the next incremental step;

[0014] Step 5: Embed the high-cycle fatigue crack extension program into the software platform for calculation; process the simulation data to obtain the extension rate curve of the fatigue crack of the intersecting node, and compare the result with the test to verify the validity of the simulation result.

[0015] In step 1, a numerical model of the circular steel pipe intersection node with initial cracks is established in the software platform based on the coordinate mapping method.

[0016] In step 2, the mesh elements with cracks are divided into three types through the level set function, namely, the elements that the cracks do not penetrate, the elements that the cracks completely penetrate, and the elements that the cracks do not completely penetrate. For the first type of elements, the displacement field calculation method is the same as that of the finite element method, while the displacement field needs to be corrected for the latter two types of elements. The specific expression is:

[0017]

[0018] In the formula, is the displacement field when the crack does not pass through the unit; is the displacement field when the crack completely passes through the unit, where a i is the node degree of freedom, H(x) is the level set function, and its calculation formula is x is an integration point, x* is the point on the crack surface closest to the integration point, and n is the normal vector of x* on the crack surface; is the displacement field when the crack does not completely penetrate the unit, b i is the node degree of freedom, F(x) is the crack incomplete penetration unit expansion function in polar coordinate system;

[0019] According to the displacement field of the grid unit, the stress at each grid unit integration point and the stress at each node of the overall grid can be obtained. The interaction J integral of the crack can be obtained through the stress field, and then the stress intensity factor of the crack can be obtained.

[0020] In step 2, since the fatigue cracks at the intersection nodes of the circular steel pipe are mixed cracks composed of type I cracks, type II cracks and type III cracks, the equivalent stress intensity factor needs to be calculated according to the stress intensity factor corresponding to the type I crack, the stress intensity factor corresponding to the type II crack and the stress intensity factor corresponding to the type III crack. The calculation formula is:

[0021]

[0022] Where B is an empirical parameter, which is taken as 1.0; ΔK I , ΔK II , ΔK III , ΔK eq They are the stress intensity factor increment and equivalent stress intensity factor increment corresponding to mode I crack, mode II crack and mode III crack respectively; the calculation method of stress intensity factor increment is:

[0023] ΔK=K max -K min

[0024] Where K max K is the stress intensity factor obtained from the maximum load under constant amplitude load, min is the stress intensity factor obtained for the minimum load under constant amplitude load.

[0025] In step 4, the fatigue crack growth criterion adopts the Paris criterion, and the criterion expression is:

[0026]

[0027] Where a is the crack length, N is the number of fatigue load cycles, C and m are material parameters; C is 2.66704×10 -11 m / circle, m is 2.75.

[0028] In step 4, the fatigue crack propagation direction adopts the three-dimensional maximum circumferential stress criterion, and the criterion expression is:

[0029]

[0030] In the formula, ΔK Ieq The equivalent stress intensity factor increment considering the influence of type III stress intensity factor is expressed as:

[0031] ΔK Ieq =ΔK I +B|ΔK II |

[0032] Where B is an empirical parameter and is taken as 1.0.

[0033] In step 4, the method for extracting the stress intensity factor and the crack front coordinates is: set the output process variables in sequence, submit the job to generate the .odb file, determine the result file path and name, extract the stress intensity factor and the crack front coordinates, and finally input the results into a .txt file.

[0034] In step 4, the calculation method of the crack extension increment of the next incremental step depends on the control method of fatigue crack extension; the control method of fatigue crack extension adopts load cycle number control or single incremental step crack maximum extension increment control;

[0035] The number of load cycles is controlled to perform a fatigue crack growth analysis every ΔN cycles of the actual load to obtain the stress intensity factor distribution of the crack front and the coordinates of the discrete points of the crack front in the next incremental step. The calculation method of the crack growth increment of this method is:

[0036] Δa i =C(ΔK eq,i ) m ΔN

[0037] The maximum crack extension increment of a single incremental step is controlled according to the distribution of stress intensity factor at the crack front, and the extension length of the point with the largest stress intensity factor is specified as the maximum extension increment Δa. max , the expansion increments of the remaining points are calculated according to the following formula:

[0038]

[0039] In step 4, assume that the lower surface of the crack is a horizontal plane, and xyz is the global coordinate system, where the xy plane is coplanar with the lower surface of the crack, and the z axis is perpendicular to the xy plane; establish a local coordinate system XYZ at any point on the crack front, where the X axis coincides with the normal direction of the point, the Y axis coincides with the tangent direction of the point, and the Z axis is perpendicular to the XY plane; at the same time, set two straight lines x at this point * and * , where x * Parallel to the x-axis, y * Parallel to the y-axis; then the calculation method for the crack front coordinates of the next incremental step is:

[0040] Δx=Δacosθ*cosα

[0041] Δy=Δacosθ*sinα

[0042] Δz=Δasinθ.

[0043] In step 4, the updating method of the crack model of the next incremental step is: sequentially establish a two-dimensional projection model of the crack front of the nth step, adjust the coordinates of the discrete points of the crack front to form a three-dimensional model, divide the grid and import the crack model of the n-1th step, and finally merge the grid nodes to form the crack model of the nth step.

[0044] The beneficial effects of the present invention are as follows: compared with the prior art, the present invention is based on the method for simulating the high-cycle fatigue crack extension of the intersecting node of the circular steel tube based on the extended finite element method, the stress intensity factor of the fatigue crack of the intersecting node is calculated by using the fracture mechanics theory, and the disadvantages of the mesh reconstruction strategy required by the finite element method are overcome by using the extended finite element method. The constructed intersecting node high-cycle fatigue crack extension program can realize the numerical simulation of the high-cycle fatigue crack extension of the intersecting node of the circular steel tube by using the extended finite element method in the existing software platform, and obtain the fatigue crack extension rate curve under the action of the constant amplitude fatigue load. The method provided by the present invention has low difficulty in implementation, high calculation efficiency, and can ensure accuracy at the same time. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 is a flow chart of the prior art;

[0046] Figure 2 is a flow chart of the present invention;

[0047] Figure 3 is a schematic diagram of a T-shaped circular steel pipe intersection node provided according to an embodiment of the present invention;

[0048] Figure 4 is a schematic diagram of components of a T-shaped circular steel pipe intersection node provided according to an embodiment of the present invention;

[0049] Figure 5is a schematic diagram of “flat plate-circular tube” coordinate mapping provided according to an embodiment of the present invention;

[0050] Figure 6 is a schematic diagram of a fatigue crack propagation direction provided according to an embodiment of the present invention;

[0051] Figure 7 is a flow chart of a method for extracting crack front stress intensity factor and crack tip coordinates according to an embodiment of the present invention;

[0052] Figure 8 is a schematic diagram of a method for calculating the coordinates of discrete points on the fatigue crack front of the next incremental step provided by an embodiment of the present invention;

[0053] Fig. 9 is a flow chart of a crack model updating method provided according to an embodiment of the present invention;

[0054] Fig.10 is a comparison diagram of fatigue crack growth rate and test provided according to an embodiment of the present invention;

[0055] Fig.11 is a comparison diagram of fatigue crack growth paths and tests provided according to an embodiment of the present invention;

[0056] Fig.12 is a comparison diagram of fatigue crack width-to-depth ratio change and test according to an embodiment of the present invention;

[0057] Fig.13 It is a schematic diagram of the final extension result of fatigue crack provided according to an embodiment of the present invention. DETAILED DESCRIPTION

[0058] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present invention.

[0059] Example 1

[0060] like Figure 2 Shown is a flow chart of the present invention, comprising the following steps:

[0061] Step 1: According to the mechanical properties and specifications of the materials used for the intersection node specimens, a numerical model of the intersection node of a circular steel pipe with an initial crack is established in the software platform;

[0062] Step 2: Using the extended finite element method and the level set function, the crack region is defined and the elements through which the crack passes are enriched to obtain the stress intensity factor at the crack front.

[0063] Step 3: Apply loads and boundary conditions;

[0064] Step 4, establishing a high-cycle fatigue crack growth program for intersecting nodes, specifically including: establishing fatigue crack growth criteria, determining fatigue crack growth direction, extracting stress intensity factor and crack front coordinates, calculating crack growth increment for the next incremental step, calculating crack front coordinates for the next incremental step, and updating crack model for the next incremental step;

[0065] Step 5: The high-cycle fatigue crack growth program is implanted into the software platform for operation. The simulation data is processed to obtain the growth rate curve of the fatigue crack of the intersecting node, and the results are compared with the test to verify the validity of the simulation results.

[0066] Example 2

[0067] This embodiment discloses a specific implementation plan based on the above embodiments.

[0068] Step 1: According to the mechanical properties and specifications of the materials used in the intersection node specimens, a numerical model of the circular steel tube intersection node with initial cracks is established in the software platform based on the coordinate mapping method. Taking the T-shaped circular steel tube intersection node as an example, the model used is as follows: Figure 3 For the T-shaped circular steel pipe intersection node shown in the figure, the component specifications and dimensions are shown in Table 1, and the mechanical properties of the steel pipe materials and weld materials are shown in Table 2.

[0069] Specifically, the C3D8R unit is used in the intersection nodes of the T-shaped circular steel pipe, and the C3D8 unit is used in the crack area. The overall model has a total of 297974 mesh elements and 429762 mesh nodes.

[0070] Table 1 Dimensions of T-shaped circular steel pipe intersection nodes

[0071]

[0072] Table 2 Material parameters of materials used in intersecting nodes

[0073]

[0074] Specifically, refer to Figure 4 The T-shaped circular steel pipe intersection node is divided into five parts, namely: branch pipe, weld and main branch transition zone 1, main pipe 2, main pipe and branch intersection area 3, initial crack 4, node fixed end 5. Correspondingly, the establishment of the T-shaped circular steel pipe intersection node model is divided into five steps: 1) obtain the branch pipe, weld and main branch transition zone through coordinate mapping; 2) obtain the main pipe model through coordinate mapping; 3) obtain the main pipe and branch intersection area model through coordinate mapping; 4) obtain the initial crack model through coordinate mapping; 5) establish the fixed end model.

[0075] Specifically, refer to Figure 5, establish the local coordinate system XYZ of the plate and the local coordinate system xyz of the circular tube, R is the radius of the circular tube. The basic principle of the coordinate mapping method is: first establish a plate model, and then convert the plate model into a circular tube model through coordinate mapping. The formula for coordinate mapping is:

[0076] x=Dcos(Y / D)

[0077] y=Dsin(Y / D)

[0078] In the formula, x and y are the coordinates in the local coordinate system of the circular tube; Y is the coordinate in the local coordinate system of the plate. For the upper surface of the plate, that is, the outer surface of the circular tube, D = R; for the lower surface of the plate, that is, the inner surface of the circular tube, D = Rt. t is the thickness of the plate.

[0079] Furthermore, the five parts of the T-shaped circular steel pipe intersection node can be mapped from the plate model to the tube model through this method. In particular, when the plate width is smaller than the circumference of the circular pipe, the non-closed circular pipe model obtained by the above formula can be called a curved plate model.

[0080] Furthermore, after the five partial models are established, a T-shaped circular steel pipe intersecting node containing an initial crack is formed through model assembly.

[0081] Step 2: Use the extended finite element method and level set function to define the crack region in order to obtain the stress intensity factor at the crack front.

[0082] Specifically, the application method of the extended finite element and level set function is as follows: through the level set function, the mesh elements containing cracks are divided into three types, namely, the crack does not penetrate the element, the crack completely penetrates the element, and the crack does not completely penetrate the element (i.e., the crack tip element). Then, for the first type of element, the same displacement field calculation method as the finite element method is used, while the displacement field needs to be corrected for the latter two types of elements. The specific expression is:

[0083]

[0084] In the formula, is the displacement field when the crack does not pass through the unit; is the displacement field when the crack completely passes through the unit, where a i is the node degree of freedom, H(x) is the level set function, and its calculation formula is x is an integration point, x* is the point on the crack surface closest to the integration point, and n is the normal vector of x* on the crack surface; is the displacement field when the crack does not completely penetrate the unit, b i is the node degree of freedom, and F(x) is the expansion function of the crack that does not fully penetrate the unit in the polar coordinate system.

[0085] According to the displacement field of the grid unit, the stress at each grid unit integration point and the stress at each node of the overall grid can be obtained. The interaction J integral of the crack can be obtained through the stress field, and then the stress intensity factor of the crack can be obtained.

[0086] Furthermore, the stress intensity factor at the crack front is calculated using the interaction integral method, and the calculation formula is:

[0087]

[0088] In the formula, K I , K II , K III are the stress intensity factors corresponding to mode I crack, mode II crack and mode III crack respectively; J I int , J II int , J III int are the interaction J-integrals respectively; B is the logarithmic energy system matrix.

[0089] Furthermore, since the fatigue cracks at the intersection nodes of the circular steel pipes are mixed cracks composed of type I cracks, type II cracks and type III cracks, it is necessary to calculate the equivalent stress intensity factor for the fatigue crack growth criterion based on the stress intensity factor corresponding to the type I crack, the stress intensity factor corresponding to the type II crack and the stress intensity factor corresponding to the type III crack. The calculation formula is:

[0090]

[0091] Where B is an empirical parameter, which is taken as 1.0; ΔK I , ΔK II , ΔK III , ΔK eq They are the stress intensity factor increment and equivalent stress intensity factor increment corresponding to type I crack, type II crack and type III crack respectively. The calculation method of stress intensity factor increment is:

[0092] ΔK=K max -K min

[0093] Where K max K is the stress intensity factor obtained from the maximum load under constant amplitude load, min is the stress intensity factor obtained for the minimum load under constant amplitude load.

[0094] It should be noted that the above are calculation methods for the stress intensity factor and equivalent stress intensity factor of a single discrete point at the crack front, and the calculation formulas for the remaining points are the same.

[0095] Specifically, when calculating the stress intensity factor of the crack front using the extended finite element method, the crack front is discretized into a finite number of points, the stress intensity factor of each point is calculated, and this is used to represent the distribution of the stress intensity factor of the entire crack front. The finite number of discrete points is determined based on the number of grid elements that pass through the crack. Therefore, during the expansion process, the number of discrete points on the crack front remains unchanged or increases.

[0096] Step 3: Apply loads and boundary conditions.

[0097] Specifically, the fatigue load is a constant amplitude load, the load is applied to the end of the branch pipe, the maximum value is 140 kN, the stress ratio is 0.05, and fixed constraints are applied to the fixed ends at both ends of the main pipe.

[0098] Step 4: Establish a high-cycle fatigue crack growth program for intersecting nodes, including: establishing fatigue crack growth criteria, determining fatigue crack growth direction, extracting stress intensity factor and crack front coordinates, calculating the crack growth increment for the next incremental step, calculating the crack front coordinates for the next incremental step, and updating the crack model for the next incremental step.

[0099] Furthermore, the fatigue crack growth criterion adopts the Paris criterion, and the criterion expression is:

[0100]

[0101] Where a is the crack length, N is the number of fatigue load cycles, C and m are material parameters, and ΔK eq is the increment of equivalent stress intensity factor. Where C is 2.66704×10 -11 m / circle, m is 2.75.

[0102] Further, see Figure 6 , the fatigue crack propagation direction adopts the three-dimensional maximum circumferential stress criterion, and the criterion expression is:

[0103]

[0104] In the formula, ΔK Ieq The equivalent stress intensity factor increment considering the influence of type III stress intensity factor is expressed as:

[0105] ΔK Ieq =ΔK I +B|ΔK II |

[0106] Where B is an empirical parameter and is taken as 1.0.

[0107] Further, the stress intensity factor and crack front coordinates are extracted by referring to Figure 7 flow chart.

[0108] Furthermore, the calculation method of the crack growth increment of the next incremental step depends on the control method of fatigue crack growth. There are two control methods for fatigue crack growth: the first is to control by the number of load cycles, and the second is to control by the maximum crack growth increment of a single incremental step.

[0109] Specifically, the former is that each cycle ΔN of the actual load is equivalent to an incremental step of the simulation method provided by the present invention, that is, a fatigue crack growth analysis is performed every ΔN cycles of the actual load to obtain the distribution of the stress intensity factor at the crack front and the coordinates of the discrete points at the crack front of the next incremental step. The calculation method of the crack growth increment of this method is:

[0110] Δa=C(ΔK eq ) m ΔN

[0111] The latter is based on the distribution of stress intensity factors at the crack front, and stipulates that the extension length of the point with the largest stress intensity factor is the maximum extension increment Δa max , then the crack growth increment at this point is:

[0112] Δa max =C(ΔK eq,max ) m ΔN

[0113] The crack extension increment at any point i on the crack front is:

[0114] Δa i =C(ΔK eq,i ) m ΔN

[0115] By dividing the above two calculation formulas and shifting the terms, we can obtain the calculation formula for controlling fatigue crack growth through the maximum crack growth increment of a single incremental step:

[0116]

[0117] This embodiment adopts the second method to control crack propagation.

[0118] Furthermore, the calculation method of the crack front coordinates for the next incremental step needs to be determined. Assuming that the discrete points of the crack front always extend along the normal direction of the point, refer to Figure 8 Assume that the lower surface of the crack is a horizontal plane, and xyz is the global coordinate system, where the xy plane is coplanar with the lower surface of the crack, and the z axis is perpendicular to the xy plane. Establish a local coordinate system XYZ at any point on the crack front, where the X axis coincides with the normal direction of the point, the Y axis coincides with the tangent direction of the point, and the Z axis is perpendicular to the XY plane. At the same time, set two straight lines x at this point. * and * , where x* Parallel to the x-axis, y * Parallel to the y-axis. Then the calculation method of the crack front coordinates of the next incremental step is:

[0119] Δx=Δa cosθ*cosα

[0120] Δy=Δa cosθ*sinα

[0121] Δz=Δa sinθ

[0122] Furthermore, the update method of the crack model in the next incremental step is as follows: Fig. 9 flow chart.

[0123] It should be noted that the above content only describes the calculation method of high cycle fatigue crack extension at one discrete point on the crack front, and the calculation method for the remaining discrete points is the same.

[0124] Step 5: Embed the high-cycle fatigue crack growth program into the software platform for calculation. Process the simulation data to obtain the growth rate curve of the fatigue crack of the intersecting node, and compare the results with the test to verify the validity of the simulation results.

[0125] Figure 10 to Figure 13 This is the simulation result of this embodiment.

[0126] Specifically, the final crack model extension results refer to Fig.10 When the crack penetrates the main pipe wall thickness, the crack length is 2c = 100.614mm and the depth is a = 12.212mm. The corresponding test results are 2c = 105mm and a = 12mm.

[0127] Specifically, the crack growth rate curve refers to Fig.11 The crack growth rate curve obtained by the method provided by the present invention is close to the test result. It should be noted that since the crack grows from the initial size, the number of load cycles obtained by simulation is smaller than the actual situation, so the number of load cycles is corrected.

[0128] Specifically, the change of crack width-to-height ratio during the expansion process refers to Fig.12 In the figure, c is half of the crack length, a is the crack depth, and T is the main pipe wall thickness. The change process of the crack aspect ratio obtained by the method provided by the present invention is similar to the test result.

[0129] Specifically, the crack propagation path results on the intersecting node surface refer to Fig.13 .

Claims

1. A numerical simulation method for high cycle fatigue of circular steel tube intersection nodes based on extended finite element, It is characterized in that The steps include: Step 1: According to the mechanical properties and specifications of the materials used for the intersection node specimens, a numerical model of the intersection node of a circular steel pipe with an initial crack is established in the software platform; Step 2: Use the extended finite element method and level set function to define the crack region to obtain the stress intensity factor at the crack front. The calculation method of the stress intensity factor is: In the formula, K I , K II , K III are the stress intensity factors corresponding to mode I crack, mode II crack and mode III crack respectively; J I int , J II int , J III int are the interaction J-integrals corresponding to mode I crack, mode II crack and mode III crack respectively; B is the logarithmic energy system matrix; Step 3: Apply loads and boundary conditions; Step 4, establishing a high-cycle fatigue crack growth program for intersecting nodes, specifically including: establishing fatigue crack growth criteria, determining fatigue crack growth direction, extracting stress intensity factor and crack front coordinates, calculating crack growth increment for the next incremental step, calculating crack front coordinates for the next incremental step, and updating crack model for the next incremental step; Step 5: Embed the high-cycle fatigue crack extension program into the software platform for calculation; process the simulation data to obtain the extension rate curve of the fatigue crack of the intersecting node, and compare the result with the test to verify the validity of the simulation result.

2. According to claim 1, the method for numerical simulation of high cycle fatigue of circular steel pipe intersection nodes based on extended finite element, It is characterized in that In step 1, a numerical model of the circular steel pipe intersection node with initial cracks is established in the software platform based on the coordinate mapping method.

3. According to claim 1, the method for numerical simulation of high cycle fatigue of circular steel pipe intersection nodes based on extended finite element, It is characterized in that In step 2, the mesh elements with cracks are divided into three types through the level set function, namely, the elements that the cracks do not penetrate, the elements that the cracks completely penetrate, and the elements that the cracks do not completely penetrate. For the first type of elements, the displacement field calculation method is the same as that of the finite element method, while the displacement field needs to be corrected for the latter two types of elements. The specific expression is: In the formula, is the displacement field when the crack does not pass through the unit; is the displacement field when the crack completely passes through the unit, where a i is the node degree of freedom, H(x) is the level set function, and its calculation formula is x is an integration point, x* is the point on the crack surface closest to the integration point, and n is the normal vector of x* on the crack surface; is the displacement field when the crack does not completely penetrate the unit, b i is the node degree of freedom, F(x) is the crack incomplete penetration unit expansion function in polar coordinate system; According to the displacement field of the grid unit, the stress at each grid unit integration point and the stress at each node of the overall grid can be obtained. The interaction J integral of the crack can be obtained through the stress field, and then the stress intensity factor of the crack can be obtained.

4. According to claim 1, the method for numerical simulation of high cycle fatigue of circular steel pipe intersection nodes based on extended finite element, It is characterized in that In step 2, since the fatigue cracks at the intersection nodes of the circular steel pipe are mixed cracks composed of type I cracks, type II cracks and type III cracks, the equivalent stress intensity factor needs to be calculated according to the stress intensity factor corresponding to the type I crack, the stress intensity factor corresponding to the type II crack and the stress intensity factor corresponding to the type III crack. The calculation formula is: Where B is an empirical parameter, which is taken as 1.0; ΔK I , ΔK II , ΔK III , ΔK eq They are the stress intensity factor increment and equivalent stress intensity factor increment corresponding to mode I crack, mode II crack and mode III crack respectively; The calculation method of stress intensity factor increment is: △K=K max -K min Where K max K is the stress intensity factor obtained from the maximum load under constant amplitude load, min is the stress intensity factor obtained for the minimum load under constant amplitude load.

5. According to claim 4, the method for numerical simulation of high cycle fatigue of circular steel pipe intersection nodes based on extended finite element, It is characterized in that In step 4, the fatigue crack growth criterion adopts the Paris criterion, and the criterion expression is: Where a is the crack length, N is the number of fatigue load cycles, C and m are material parameters; C is 2.66704×10 - 11 m / circle, m is 2.

75.

6. According to claim 4, the method for numerical simulation of high cycle fatigue of circular steel pipe intersection nodes based on extended finite element, It is characterized in that In step 4, the fatigue crack propagation direction adopts the three-dimensional maximum circumferential stress criterion, and the criterion expression is: In the formula, ΔK Ieq The equivalent stress intensity factor increment considering the influence of mode III stress intensity factor is expressed as: △K Ieq =△K I +B|△K II | Where B is an empirical parameter and is taken as 1.

0.

7. According to claim 4, the method for numerical simulation of high cycle fatigue of circular steel pipe intersection nodes based on extended finite element, It is characterized in that In step 4, the method for extracting the stress intensity factor and the crack front coordinates is: set the output process variables in sequence, submit the job to generate the .odb file, determine the result file path and name, extract the stress intensity factor and the crack front coordinates, and finally input the results into a .txt file.

8. According to claim 4, the method for numerical simulation of high cycle fatigue of circular steel pipe intersection nodes based on extended finite element, It is characterized in that In step 4, the calculation method of the crack extension increment of the next incremental step depends on the control method of fatigue crack extension; the control method of fatigue crack extension adopts load cycle number control or single incremental step crack maximum extension increment control; The number of load cycles is controlled to perform a fatigue crack growth analysis every ΔN cycles of the actual load to obtain the stress intensity factor distribution of the crack front and the coordinates of the discrete points of the crack front in the next incremental step. The calculation method of the crack growth increment of this method is: △a i =C(△K eq,i ) m △N The maximum crack extension increment of a single incremental step is controlled according to the distribution of stress intensity factor at the crack front, and the extension length of the point with the largest stress intensity factor is specified as the maximum extension increment Δa. max , the expansion increments of the remaining points are calculated according to the following formula:

9. The method for numerical simulation of high cycle fatigue of circular steel pipe intersection nodes based on extended finite element according to claim 4, It is characterized in that In step 4, assume that the lower surface of the crack is a horizontal plane, and xyz is the global coordinate system, where the xy plane is coplanar with the lower surface of the crack, and the z axis is perpendicular to the xy plane; establish a local coordinate system XYZ at any point on the crack front, where the X axis coincides with the normal direction of the point, the Y axis coincides with the tangent direction of the point, and the Z axis is perpendicular to the XY plane; at the same time, set two straight lines x at this point * and * , where x * Parallel to the x-axis, y * parallel to the y-axis; then the calculation method for the crack front coordinates of the next incremental step is: △x=△acosθ*cosα △y=△acosθ*sinα △z=△asinθ.

10. The method for numerical simulation of high cycle fatigue of circular steel pipe intersection nodes based on extended finite element according to claim 4, It is characterized in that In step 4, the updating method of the crack model of the next incremental step is: sequentially establish a two-dimensional projection model of the crack front of the nth step, adjust the coordinates of the discrete points of the crack front to form a three-dimensional model, divide the grid and import the crack model of the n-1th step, and finally merge the grid nodes to form the crack model of the nth step.

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